Hadamard Property of the in and out States for Klein–Gordon Fields on Asymptotically Static Spacetimes

2016/09/30 by Christian Gérard, Michał Wrochna · 19 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Bounded function #Cauchy distribution #Class (philosophy) #Computer science #Hadamard matrix #Hadamard three-lines theorem #Hadamard transform #Klein–Gordon equation #Mathematical analysis #Mathematical physics #Mathematics #Physics #Property (philosophy) #Pure mathematics #Quantum mechanics #Range (aeronautics) #Spectral Theory in Mathematical Physics #advanced mathematical theories #hep-th #math-ph #math.AP #math.MP

paper · pdf · doi:10.1007/s00023-017-0573-2

published in Annales Henri Poincaré 18(8), 2715-2756 (Birkhäuser) · First part of a splitted and extended version of a manuscript which was originally arXiv:1603.07465; v2: various minor improvements, accepted in AHP

openalex created_date 2016/07/22 · arxiv created 2017/02/21 · openalex publication_date 2017/04/06 · arxiv updated 2018/03/28 · openalex updated_date 2026/08/05

Abstract

We consider the massive Klein-Gordon equation on a class of asymptotically static spacetimes (in the long range sense) with Cauchy surface of bounded geometry. We prove the existence and Hadamard property of the in and out states constructed by scattering theory methods.

Citations

• Feynman propagators and Hadamard states from scattering data for the Klein-Gordon equation on asymptotically Minkowski spacetimes
• Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces
• The Hadamard Condition for Dirac Fields and Adiabatic States on Robertson-Walker Spacetimes
• Spinor Structure of Space-Times in General Relativity. I
• Equivalence of the (Generalised) Hadamard and Microlocal Spectrum Condition for (Generalised) Free Fields in Curved Spacetime
• Global hyperbolicity and completeness
• Generalized cylinders in semi-Riemannian and spin geometry
• Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property
• MICROLOCAL SPECTRUM CONDITION AND HADAMARD FORM FOR VECTOR-VALUED QUANTUM FIELDS IN CURVED SPACETIME
• Fourier integral operators. II